Magnet configurations

ABSTRACT

A magnet array is disclosed comprising a plurality of polyhedral magnets arranged in a Halbach cylinder configuration, the centers of individual ones of the plurality of polyhedral magnets being arranged substantially in a plane in a magnet rack, the plurality of the polyhedral magnets at least partly enclosing a testing volume, and comprising a first plurality of polyhedral magnets arranged in a Halbach cylinder configuration and a second plurality of polyhedral magnets arranged in a non-Halbach configuration. In another aspect, a magnet array is disclosed comprising a first subset and a second subset of polyhedral magnets having different coercivities. In yet another aspect, a magnet array is disclosed wherein a subset of the centers of the individual ones of the plurality of polyhedral magnets are laterally displaced from a nominal position in the magnet rack to counteract a magnetic field gradient of the magnet array.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority of U.S. provisional patent application62/891336 filed on Aug. 24, 2019, the specification of which is herebyincorporated by reference in its entirety.

BACKGROUND (a) Field

The present disclosure relates to magnet configurations. Moreparticularly, it relates to modified Halbach magnet configurations.

(b) Related Prior Art

In a nuclear magnetic resonance (NMR) experiment, a sample for analysisis placed under the influence of a biasing static magnetic field, whichpartially aligns the sample's nuclear-spin magnetic moments. The momentsprecess in the static field at a frequency, called the Larmor frequency,which is proportional to the field strength. The magnetic moments of thesample can be manipulated by applying a transverse radio frequency (RF)magnetic field at the Larmor frequency. By observing the reaction of thesample to the RF field, insight into the chemical composition of thesample can be gained. The power of NMR as an analytical method may belargely a function of how well the characteristics of the appliedmagnetic fields can be controlled.

The practice of shimming magnetic fields (rendering the fields moreuniform) has existed since the earliest days of NMR and originally usedthin pieces of metal physically placed behind source magnets to adjustthe positions of those magnets to refine the magnetic field. More modernshimming techniques use electro-magnetic coils. Conventional high-fieldmagnetic resonance spectrometers commonly use shimming coils disposed onsubstantially cylindrical coil forms. In contrast, the use of shimming(shim) coils in compact NMR devices has proved difficult primarily dueto space restrictions that may not accommodate traditional shim coilsystems, which can have many layers. The space available inside a mainmagnet in many such devices may be too small to accommodate a typicalset of shimming coils whose individual elements are each designedpredominantly to address one and only one geometrical aspect orgeometrical component of the residual inhomogeneity of the main magneticfield.

FIGS. 1A, 1B, and 1C compare the main biasing field and sample tubeconfigurations of typical high-field spectrometer designs with a designfor compact magnet systems that is based on a cylindrical Halbach array.The arrows labelled B indicate the main magnetic field direction. Noshimming measures are shown in the figures. FIG. 1A schematically showsthe superconducting field coils of the high-field magnet, an insertedcylindrical sample tube, and the field, B, produced by the coils. Themagnetic field within the sample volume is aligned along the commonsymmetry axis of the coils and the tube.

FIGS. 1B and 1C show the same sample tube inserted into a cylindricalHalbach magnet array, which produces a field, B, perpendicular to thesymmetry axis of the tube. This particular Halbach array is composed ofeight magnets in a circular (as shown in FIG. 1B) arrangement placedaround the tube, with the magnetization vectors of the magnets (shown asarrows) perpendicular to the tube's symmetry axis. The magnetizationvector is a quantitative and directional representation of thepolarization of magnetic dipoles in a material. The field inside theHalbach array is quite uniform for some applications but can be tooinhomogeneous for some high-resolution NMR experiments.

In order to substantially reduce the inhomogeneity of a magnetic field,it may be helpful to have independent control over different geometricalaspects of the field inhomogeneity. In many magnetic resonanceapplications, the main magnetic field is strongly polarized along aspecified direction. Within this application, as is common practice inthe art, this direction is understood to be the z-axis in a Cartesianreference frame in which the origin is at some fixed point, for examplenear the center of a sample under study. The Larmor frequency ofmagnetic spins located at a point in space is determined by themagnitude of the field at that point, which in reasonably homogeneousfields is very well approximated by the z-component of the field, B_(z).One can expand B_(z) as a scaled sum of functions,

B _(z)(x,y,z)=B ₀+Σ_(k) c _(k)ƒ_(k)(x,y,z),

where k is a variable (or a number of variables) used to index thevarious functions, ƒ_(k), in the set, and where x, y, and z areCartesian or other spatial coordinates defining positions within avolume enclosing at least part of the sample. B₀ is the large andspatially uniform part of the field, and the coefficients, c_(k),quantify different components of the field inhomogeneity. Such sets offunctions, for example x, z, xy, (x²−y²) are said to be orthogonal (withrespect to a specified scalar product of functions) if the scalarproduct between two functions that are not the same is zero. A commonscalar product between two functions is the integral,

<k ₁ |k ₂>=∫_(v) W(x,y,z)ƒ_(k) ₁ (x,y,z)ƒ_(k) ₂ *(x,y,z)dV,

where V denotes a volume relevant to the functions over which theintegral is calculated, where the star denotes complex conjugation, andwhere W denotes a weighting function defined on the volume, whichquantifies how important the volume element at (x, y, z) is in itscontribution to the integral.

For example, commonly, an expansion in spherical harmonic functions isused, where the functions are

ƒ_(n,m)(x, y, z)=N _(n,m) P _(n,m)(cos θ)exp(im ϕ),

where θ=tan⁻¹(√{square root over (x²+y²)}/z) and ϕ=tan⁻¹(y/x), whereP_(n,m) denotes a Legendre polynomial or associated Legendre function,and where N_(n,m) are normalization factors. The functions are said tobe “orthogonal over the unit sphere.” Sometimes, real-valued linearcombinations of the complex-valued spherical harmonic functions are usedinstead. If, in addition, the scalar product between each function ƒ_(k)and itself is equal to 1, then the set of functions is said to beorthonormal. Use of orthogonal or orthonormal functions can facilitatedescription and analysis of field imperfections and can be helpful indesigning and implementing systems for control of the quality of thefield in applications.

Well-controlled magnetic fields are particularly important in nuclearmagnetic resonance (NMR) spectroscopy and other magnetic resonance (MR)applications. In many NMR spectroscopy experiments, a strong, staticmagnetic field is applied in a region of space that contains a sampleunder study, and it is desirable that this field be as spatially uniformas possible in order to observe important but subtle variations in themagnetic response of the sample. It is also desirable in many NMRapplications to have a static magnetic field that is as strong as ispractical.

At least three classes of magnets have been used to provide strong,static magnetic fields in NMR devices: superconducting electromagnets,resistive electromagnets, and permanent magnets. Permanent magnets orarrays (also called assemblies or configurations) thereof can beadvantageous in applications where low cost, low maintenance and/orportability are desirable.

In practice, permanent magnets are often accompanied by pole pieces,which are pieces of magnetically permeable material placed in thevicinity of magnets in order to contribute to or shape a magnetic field.In some applications, it is desirable that materials used for polepieces be magnetically “soft,” that is, that they have a relatively lowcoercivity. It is also desirable in some applications that pole piecematerials be strongly magnetized when placed in a magnetic field, thatis, that they have a high saturation magnetization.

One design for producing a substantially strong magnetic field in asmall volume is the Halbach cylinder, wherein magnetic dipoles withinhigh-coercivity permanent magnet materials are arranged around a centralcavity. FIG. 2 shows a cross-sectional view of an idealization of aHalbach cylinder 10, along with a coordinate system 12 that is used tocompute and select the orientations of magnetic dipoles, shown as arrows14, within a region surrounding a central volume 16. In the idealizedHalbach cylinder, magnetization direction {circumflex over (m)} isposition-dependent according to the equation,

{circumflex over (m)}(ρ, ϕ, z)=cos(kϕ){circumflex over(ρ)}+sin(kϕ){circumflex over (ϕ)},

in cylindrical polar coordinates ρ, φ, z, with integer parameter k=1 forthe most prevalent case, which produces a substantially uniform field inthe central volume 16. Other choices of k provide different, non-uniformfield configurations. In practical implementations, discrete componentmagnets are used as an approximation to the continuously varyingmagnetization suggested by FIG. 2.

FIGS. 3A, 3B, 3C and 3D show example prior art implementations ofHalbach-cylinder-based magnet configurations. FIG. 3A (adapted from F.Bertora, A. Trequattrini, M. G. Abele, and H. Rusinek, “Shimming ofyokeless permanent magnets designed to generate uniform fields,” Journalof Applied Physics 73, 6864, 1993) shows a cylindrical configuration ofmagnets designated 20 surrounding space 24, that makes efficient use ofspace and employs many oblique shapes 21, 22, 23 in its design.

FIG. 3B (adapted from E. Danieli, J. Mauler, J. Perlo, B. Blumich, andF. Casanova, “Mobile sensor for high resolution NMR spectroscopy andimaging, Journal of Magnetic Resonance 198, 80, 2009) shows an array 30that uses permanent magnets of the same cubic shape 31 to enclose space32. However, this implementation suffers from low packing density.

When the space surrounding a central volume is broken up into regions,the individual component magnets placed therein may exhibit obliqueshapes, such as those shown in FIG. 3A, that are difficult or expensiveto fabricate with high tolerance. The magnetizations required within thecomponent magnets may also be difficult to control with precisionsufficient to ensure the quality of the magnetic field within thecentral volume. If, instead, simpler component magnets such as cubes areused, as in FIG. 3B, these can be fabricated and magnetized with highprecision straightforwardly, but the geometrical constraints for somedesigns can result in a low packing density, with an attendant reductionin the field strength that can be produced.

FIG. 3C is a cross section of an embodiment of a Halbach cylinder 40comprising an array of closely packed hexagonal prisms 41 surroundingcentral space 42, disclosed in U.S. Pat. No. 8,712,706 to Leskowitz, etal., incorporated herein by reference in its entirety. FIG. 3D (alsodisclosed in U.S. Pat. No. 8,712,706), shows the general arrangement 50of individual main magnets 52 in a magnet array around a channel 53 inwhich pole pieces 54 and a sample 56 are positioned. FIG. 3D alsoillustrates the positioning of shim panels 58 on the pole pieces 54.Arrows 59 show the predominant magnetization directions of each mainmagnet 52 in the arrangement.

In a Halbach cylinder model, the ideal is an infinitely long cylinder.In practice, the cylinder is of finite length, which can lead to varioustechnical problems and undesirable features in the primary magneticfield of the array, and designs attempting to overcome thesedisadvantages can be complex. An alternative approach for producinghomogeneous fields uses a Halbach sphere, practical embodiments of whichhave been suggested by H. Leupold in U.S. Pat. No. 4,837,542.

FIG. 4A, adapted from U.S. Pat. No. 9,952,294 to Leskowitz, incorporatedherein by reference in its entirety, shows a sphere 60 enclosing acentral cavity 62 and having local magnetic dipole orientations 64. Oncea desired magnetic field axis, {circumflex over (v)}, is selected, therequired magnetization directions for the component magnets in theassembly can be calculated by establishing a spherical polar coordinatesystem 66 with colatitude angle θ=0 along the magnetic field direction{circumflex over (v)}, then calculating the magnetization direction{circumflex over (m)} for the given magnet's center coordinatesaccording to formulas disclosed in U.S. Pat. No. 9,952,294 to Leskowitz.

In order to best approximate a uniform field in the idealized case,magnetization direction {circumflex over (m)} within the spherical shellsurrounding the central cavity is position-dependent according to theequation,

{circumflex over (m)}(r, θ, φ)=cos(kθ){circumflex over(r)}+sin(kθ){circumflex over (θ)},

in spherical polar coordinates r, θ, ϕ), again with parameter k=1 forthe uniform-field case.

It will be observed that magnetization in the spherical case differsfrom the magnetization in the cylindrical case. In the Halbach spheremodel, the magnetization of the dipole at a position {right arrow over(r)}=r{circumflex over (r)} lies in the meridional plane spanned by{circumflex over (r)} and {circumflex over (θ)}, but in the Halbachcylinder model, the magnetization lies in a plane spanned by {circumflexover (ρ)}=(r{circumflex over (r)}−z{circumflex over (z)})/ρ, the unitvector directed away from the cylindrical symmetry axis, and {circumflexover (ϕ)}, the azimuthal unit vector. In the idealized Halbach cylindercase, the magnetization direction has no {circumflex over (z)} component(along the cylindrical symmetry axis) and is independent of the zcoordinate of the dipole's position. A variety of numericalrepresentations of such position-dependent magnetizations are possibleand will be readily identified and understood.

Spherical assemblies can be composed of combinations of magnets havingcomplex shapes, as illustrated in FIG. 4B (adapted from U.S. Pat. No.4,837,542 to Leupold). In FIG. 4B it will be seen that the sphere 70comprises multiple component primary magnets 72 having chosen dipoleorientations 74 and surrounding central cavity 76. In order to achievethe desired configuration and field, a large number of different primarymagnets having different shapes and magnetic orientations is required.Again, these can be challenging or impractical to fabricate with hightolerance.

Magnet arrays and methods for generating magnetic fields are disclosedin U.S. Pat. No. 9,952,294 to Leskowitz, including a magnet arraycomprising a plurality of polyhedral magnets arranged in a latticeconfiguration and at least partly enclosing a testing volume, the magnetarray having an associated magnetic field with a designated fielddirection {circumflex over (v)}, wherein the magnetization direction{circumflex over (m)} of an individual polyhedral magnet located at adisplacement vector {right arrow over (r)} from an origin point in thetesting volume is determined by the formula:

{circumflex over (m)}=(2({circumflex over (v)}·{right arrow over(r)}){circumflex over (r)}−({right arrow over (r)}·{right arrow over(r)}){circumflex over (v)})/({right arrow over (r)}·{right arrow over(r)}).

In embodiments the polyhedral magnets 101 are truncated cubes, and themagnet array 100 is based on a simple cubic lattice, as illustrated inFIG. 4C (adapted from U.S. Pat. No. 9,954,294 to Leskowitz). As will beseen in FIG. 4C, some of the polyhedral magnets 101 comprised in thelattice configuration making up the magnet array 100 are larger firstmagnets 103 and others are smaller second magnets 106. The smallersecond magnets 106 form composite magnets 104 at particular sites in thearray. As will be seen in FIG. 4C, the use of such smaller secondmagnets 106 is exploited to provide a sample channel 107, in this caseoriented along a body diagonal of the array.

In practice, a Halbach sphere configuration can produce a magnetic fieldthat is larger than that produced by a Halbach cylinder configuration.However, Halbach sphere configurations can suffer from limited access tothe central region of the magnet compared to Halbach cylinderconfigurations.

In applications such as magnetic resonance applications, it may beadvantageous to use the largest magnetic fields that are practical. Oneway to increase the field present inside a Halbach cylinder magnetconfiguration is to insert pole pieces into the bore of the Halbachcylinder magnet configuration. U.S. Pat. No. 9,341,690 to Leskowitz andMcFeetors discloses shaped pole pieces in a cylindrical Halbach magnetconfiguration. While inserting pole pieces into a cylindrical Halbachmagnet may increase the field, it may also create or exacerbatedeleterious magnetic field gradients, including quadratic fieldgradients. This can be partially mitigated by forming the pole pieces sothat each has a channel on its rear face, that is, a first face of thepole piece that is opposite a second face of the pole piece that isclosest to the center of the Halbach cylinder, which may be configuredas a sample location. A problem to be solved is that introducing thisback channel in the pole piece can reduce the field strength within thesample location, because magnetic material is effectively removed informing the channel.

Another way to increase the field present inside a Halbach cylindermagnet configuration is to increase the number of component magnets thatare used to constitute the magnet configuration. Such component magnetsmay be configured in concentric ring structures. For example, FIG. 3Dexhibits a single hexagonal ring of six magnets, and FIG. 3C exhibits ahexagonal ring of six magnets surrounded by a hexagonal ring of twelvemagnets. It will be readily appreciated that each component magnet issubject to magnetic interaction with the total magnetic field generatedby all the other magnets in an assembly. In particular, a componentmagnet may be located at a site where the total magnetic field generatedby the other magnets is substantially aligned with the magnetization ofsaid component magnet. In that case, said component magnet would beunder relatively low coercive stress and would therefore be subject to aweak demagnetizing force. Conversely, a component magnet may be locatedat a site where the total magnetic field generated by the other magnetsis substantially aligned away from or opposing the magnetization of saidcomponent magnet. In that case, said component magnet would be underrelatively high coercive stress and would therefore be subject to astrong demagnetizing force. Mitigating or controlling demagnetizingforces is a critical issue in determining the stability and performanceof magnet arrays in applications. Moreover, elevated coercivity can beassociated with increased cost.

There remains a need for a solution that allows for increased magneticfields while maintaining the low-cost, convenience, andmanufacturability of cylindrical and spherical Halbach magnetconfigurations.

SUMMARY

The present disclosure describes modified Halbach magnet configurations.In this disclosure, magnet configurations may also be called magnetarrays or magnet assemblies. The term “modified” Halbach magnetconfiguration means a configuration (or arrangement) of individualcomponent magnets that comprises two or more subsets of magnets, atleast one subset being configured in a Halbach cylinder magnetconfiguration and at least one other subset having another (non-Halbach)magnet configuration as discussed in this disclosure. Further, themodified Halbach magnet configurations are understood to in some wayincrease the strength, the uniformity, or both, of the magnetic fieldproduced by the magnet configuration.

Embodiments in this disclosure in which Halbach magnet configurationshave been changed comprise magnet configurations having at least twogroups of polyhedral magnets, one group arranged in a Halbach cylinderconfiguration and one group arranged in a non-Halbach cylinderconfiguration. Other embodiments in this disclosure comprise magnetconfigurations having at least two groups of polyhedral magnets havingdifferent magnetic coercivities. Further embodiments in this disclosurein which Halbach magnet configurations have been changed comprise magnetconfigurations having polyhedral magnets arranged in a Halbach cylinderconfiguration and wherein a subset of the polyhedral magnets arelaterally displaced from a nominal position to counteract a magneticfield gradient of the magnet configuration. Even further embodiments inthis disclosure in which Halbach cylinder magnet configurations havebeen changed comprise magnet configurations having composite polyhedralmagnets, each of whose component magnets has its own magnetizationvector orientation. These modified Halbach magnet configurations mayprovide an increased magnetic field produced by the magnet configurationand may influence (emphasize or de-emphasize) magnetic field gradients,including magnetic field gradients generated by introducing one or morepole pieces into the magnet configuration. These modified Halbach magnetconfigurations provide a solution that allows for increased magneticfields while accounting for cost, convenience, and manufacturability.

In one aspect there is provided a magnet array comprising: a firstplurality of polyhedral magnets arranged in a Halbach cylinderconfiguration, the centers of individual ones of the plurality ofpolyhedral magnets arranged substantially in a plane in a magnet rack ofthe magnet array, the plurality of polyhedral magnets at least partlyenclosing a testing volume; and a second plurality of polyhedral magnetsin the magnet rack, the second plurality of magnets arranged in anon-Halbach configuration.

In an embodiment, the second plurality of polyhedral magnets in themagnet rack comprising magnets having an in-plane magnetization vector,an out-of-plane magnetization vector, or a combination thereof.

In an embodiment, the magnet array has an associated magnetic field witha designated field direction v{circumflex over ( )}, wherein themagnetization direction m {circumflex over ( )} of at least one of thesecond plurality of polyhedral magnets located at a displacement vectorr {right arrow over ( )} from an origin point in the testing volume isdetermined by the formula:

{circumflex over (m)}=(2({circumflex over (v)}·{right arrow over(r)}){circumflex over (r)}−({right arrow over (r)}·{right arrow over(r)}){circumflex over (v)})/({right arrow over (r)}·{right arrow over(r)})

where r{circumflex over ( )} is the unit vector pointing along r {rightarrow over ( )}.

In an embodiment, individual ones of said polyhedral magnets areselected from the group consisting of: a truncated cube, a rhombicdodecahedron, a Platonic solid, an Archimedean solid, a Johnson solid, aprism, a chamfered polyhedron, and a truncated polyhedron.

In an embodiment, the second plurality of polyhedral magnets comprisingmagnets that are obliquely edge magnetized, obliquely vertex magnetized,axially magnetized, or a combination thereof.

In an embodiment, the first plurality of magnets comprising magnets thatare diametrically face magnetized, diametrically edge magnetized, or acombination thereof.

In an embodiment, the first and second pluralities of polyhedral magnetsare hexagonal prismatic magnets.

In an embodiment, the magnet array comprises a plurality of magnet racksarranged in a rack stack. In an embodiment, The magnet array comprisesfour magnet racks. In another embodiment, the magnet array comprisescomprising five magnet racks.

In an embodiment, the magnet racks each comprise thirty-six hexagonalprismatic magnets.

In an embodiment, the thirty-six hexagonal prismatic magnets arranged ininner, middle, and outer rings of six, twelve and eighteen hexagonalprismatic magnets, respectively, wherein the inner hexagonal prismaticmagnets are closest to the testing volume.

In an embodiment, the magnet rack comprises a cell framework and aframework housing.

In an embodiment, the magnet rack and the first and second pluralitiesof polyhedral magnets each have a height of 1.5″.

In an embodiment, cells in the cell framework having a width of 1.25″and walls of the cell framework having a thickness of 0.030″.

In an embodiment, the first plurality of polyhedral magnets comprise theinner and middle rings of six and twelve hexagonal prismatic magnets,respectively.

In an embodiment, the second plurality of polyhedral magnets comprisingpositions in the outer ring of eighteen hexagonal prismatic magnets.

In an embodiment, at least one of the individual magnet racks in therack stack comprises twenty-two diametrically face magnetized magnets,eight obliquely vertex magnetized magnets, four obliquely edgemagnetized magnets, and two axially magnetized magnets.

In an embodiment, a first magnet rack arranged above a central magneticreflection plane of the rack stack has a first magnet configuration thatis a magnetic reflection of a second magnet configuration of a secondmagnet rack arranged below the central magnetic reflection plane of therack stack.

In an embodiment, a first of the five magnet racks in the rack stack hasa magnet configuration that is a magnetic reflection of that of a fifthof the five magnet racks in the rack stack.

In an embodiment, the first plurality of polyhedral magnets in each ofthe first and fifth magnet racks comprising eighteen magnets having anin-plane magnetization vector, and the second plurality of polyhedralmagnets in each of the first and fifth magnet racks comprising eighteenmagnets having an out-of-plane magnetization vector.

In an embodiment, the eighteen in-plane magnetized magnets comprisefourteen diametrically face magnetized magnets and four diametricallyedge magnetized magnets.

In an embodiment, the eighteen magnets having an out-of-planemagnetization vector are axially magnetized.

In an embodiment, a second of the five magnet racks in the rack stackhas a configuration that is a magnetic reflection of that of a fourth ofthe five magnet racks in the rack stack.

In an embodiment, the first and second pluralities of polyhedral magnetsin each of the second, third and fourth magnet racks comprise magnetshaving an in-plane magnetization vector.

In an embodiment, each of the second and fourth magnet racks comprisetwenty-eight diametrically face magnetized magnets and eightdiametrically edge magnetized magnets.

In an embodiment, the third magnet rack comprises twenty diametricallyface magnetized magnets and sixteen diametrically edge magnetizedmagnets.

In an embodiment, the magnet array further comprises a first subset ofpolyhedral magnets and a second subset of polyhedral magnets, whereinthe first subset and the second subset of polyhedral magnets havedifferent magnetic coercivities.

According to another aspect there is provided a magnet array comprising:a first plurality of polyhedral magnets arranged in a Halbach cylinderconfiguration, the centers of individual ones of the plurality ofpolyhedral magnets arranged substantially in a plane in a magnet rack ofthe magnet array, the plurality of polyhedral magnets at least partlyenclosing a testing volume; a second plurality of polyhedral magnets inthe magnet rack, the second plurality of magnets arranged in anon-Halbach configuration; and at least one composite magnet.

In an embodiment, the at least one composite magnet includes two or moremagnets each having a different magnetization vector and the two or moremagnets are together sized and shaped to be positioned in an individualcell of the magnet array.

In an embodiment, the magnet array further comprises at least onecomposite magnet.

In an embodiment, the at least one composite magnet is a hexagonalprismatic magnet.

In an embodiment, the at least one composite magnet includes two magnetseach having a different magnetization vector.

In an embodiment, the at least one composite magnet includes more thantwo magnets each having a different magnetization vector.

In an embodiment, the magnetization vectors are selected from the groupconsisting of: diametrically face magnetized, diametrically edgemagnetized, obliquely edge magnetized, obliquely vertex magnetized, andaxially magnetized.

In an embodiment, the two or more magnets are together sized and shapedto be positioned in an individual cell of the magnet array.

According to a further aspect there is provided a magnetic resonancedevice comprising a magnet array comprising a first plurality ofpolyhedral magnets arranged in a Halbach cylinder configuration, thecenters of individual ones of the plurality of polyhedral magnets beingarranged substantially in a plane in a magnet rack of the magnet array,the plurality of polyhedral magnets at least partly enclosing a testingvolume, and a second plurality of polyhedral magnets in the magnet rack,the second plurality of magnets arranged in a non-Halbach configuration.

According to another aspect there is provided a method for assembling amagnet array, comprising: providing a first plurality of polyhedralmagnets; arranging the first plurality of polyhedral magnets in aHalbach cylinder configuration in a magnet rack, the centers ofindividual ones of the plurality of polyhedral magnets being arrangedsubstantially in a plane in the magnet rack, the plurality of polyhedralmagnets at least partly enclosing a testing volume; providing a secondplurality of polyhedral magnets; arranging the second plurality ofpolyhedral magnets in a non-Halbach configuration in the magnet rack;and arranging the magnet rack in a rack stack to assemble the magnetarray.

According to another aspect there is provided a magnet array comprising:a plurality of polyhedral magnets arranged in a magnet configuration,the plurality of polyhedral magnets comprising a first subset ofpolyhedral magnets and a second subset of polyhedral magnets, theplurality of polyhedral magnets at least partly enclosing a testingvolume, and wherein the first subset and the second subset of polyhedralmagnets have different magnetic coercivities.

In an embodiment, individual ones of the polyhedral magnets in the firstsubset have similar magnetic coercivities.

In an embodiment, the magnet array comprises one or more further subsetsof polyhedral magnets, wherein each of the subsets of polyhedral magnetshave different magnet coercivities, and the individual ones of thepolyhedral magnets within each subset have similar magnet coercivities.

In an embodiment, the individual ones of the polyhedral magnets in agiven subset are said to have similar magnetic coercivities relative toone another when a variation in magnetic coercivities associated withthe individual ones of the polyhedral magnets in the given subset doesnot exceed 5% and preferably does not exceed 2%.

In an embodiment, two or more polyhedral magnets or subsets ofpolyhedral magnets are said to have different magnetic coercivities whena difference between the magnetic coercivities exceeds a threshold of10% and preferably exceeds a threshold of 20%.

In an embodiment, the first subset of polyhedral magnets has a highercoercivity than the second subset of polyhedral magnets.

In an embodiment, the first subset of polyhedral magnets having thehigher coercivity is positioned closer to the testing volume and thesecond subset of polyhedral magnets having the lower coercivity ispositioned farther from the testing volume.

In an embodiment, the number of polyhedral magnets and the location inthe magnet array of the polyhedral magnets in the first subset and thesecond subset are selected according to a simulation.

In an embodiment, the magnet array comprises thirty-six polyhedralmagnets arranged in inner, middle, and outer rings of six, twelve andeighteen hexagonal prismatic magnets, respectively, and with four to sixof the inner hexagonal prismatic magnets being closest to the testingvolume and having the highest coercivity.

In an embodiment, each one of the plurality of polyhedral magnets has anintrinsic coercivity H_(c,i) that exceeds a threshold coercivity H_(T).

In an embodiment, selection of individual ones of the polyhedral magnetsdefining the first subset and the second subset is based on symmetryconsiderations associated with magnet positions in the magnet array.

In an embodiment, at least a portion of the polyhedral magnets arearranged in a Halbach configuration.

According to further aspect there is provided a method of determining athreshold coercivity for one or more magnets in a magnet arraycomprising a plurality of polyhedral magnets arranged in a magnetconfiguration, the plurality of polyhedral magnets comprising a firstsubset of polyhedral magnets and a second subset of polyhedral magnets,the plurality of polyhedral magnets at least partly enclosing a testingvolume, and wherein the first subset and the second subsect ofpolyhedral magnets have different magnetic coercivities, the methodcomprising:

-   -   a. simulating an initial arrangement of the plurality of        polyhedral magnets in the magnet array, each individual        polyhedral magnet having a given magnet array position and an        initial magnetization vector orientation;    -   b. choosing a set of points {right arrow over (r)} within the        volume of at least one individual polyhedral magnet in the        magnet array;    -   c. simulating, for the at least one individual polyhedral        magnet, a magnetic field intensity {right arrow over (H)}({right        arrow over (r)}) at each one of the points in the set {right        arrow over (r)}, and assigning a magnetization {right arrow over        (M)}({right arrow over (r)})at each one of the points in the set        {right arrow over (r)};    -   d. calculating a dot product {right arrow over (H)}({right arrow        over (r)})·{right arrow over (M)}({right arrow over (r)}) at        each one of the points in the set {right arrow over (r)};    -   e. selecting the minimum (most negative) value of the dot        product [{right arrow over (H)}({right arrow over (r)})·{right        arrow over (M)}({right arrow over (r)})]_(min) for the at least        one individual polyhedral magnet in the magnet array; and    -   f. determining the threshold coercivity according to the formula

$H_{T} = {{- \mu_{0}}\frac{\left\lbrack {{\overset{\rightarrow}{H}\left( \overset{\rightarrow}{r} \right)}{\overset{\rightarrow}{M}\left( \overset{\rightarrow}{r} \right)}} \right\rbrack_{\min}}{{\alpha\left( {1 - {k\Delta T}} \right)}B_{r}}}$

for the at least one individual polyhedral magnet in the magnet array.

In an embodiment, the method further comprises before performing step a,determining one or more symmetry classes of the magnet array andassigning each of the plurality of polyhedral magnets in the magnetarray to a corresponding one of the symmetry classes; and assigning thevalue of the threshold coercivity H_T determined in step f to all themagnets in the symmetry class associated with the at least oneindividual polyhedral magnet.

In an embodiment, each magnet position in a given symmetry class isrelated to other magnet positions in the same symmetry class by asymmetry element selected from the group consisting of: reflectionplane, rotation axis, rotation-reflection axis, inversion center,magnetic reflection plane, magnetic rotation axis, magneticrotation-reflection axis, and magnetic inversion center.

In an embodiment, the method further comprises identifying a maximumcoercivity H_(max) for the at least one individual polyhedral magnet;selecting an alternative {right arrow over (M)}_(alt) to the initialmagnetization vector orientation for the at least one individualpolyhedral magnet if the threshold coercivity H_(T) calculated in stepf. exceeds the maximum coercivity H_(max); and repeating steps b.through f.

According to another aspect, there is provided a method for assembling amagnet array, comprising: determining a threshold coercivity H_(T)according to claim 44 for each of the plurality of polyhedral magnets inthe given magnet array positions in the magnet array; and arranging aset of polyhedral magnets in the magnet array, wherein each individualone of the set of polyhedral magnets has a coercivity exceeding thecalculated threshold coercivity H_(T) for the given magnet arraypositions to assemble the magnet array.

According to a further aspect, there is provided a magnetic resonancedevice comprising a magnet array comprising a plurality of polyhedralmagnets arranged in a magnet configuration, the plurality of polyhedralmagnets comprising a first subset of polyhedral magnets and a secondsubset of polyhedral magnets, the plurality of polyhedral magnets atleast partly enclosing a testing volume, and wherein the first subsetand the second subset of polyhedral magnets have different magneticcoercivities.

According to a yet another aspect, there is provided a magnet arraycomprising: a plurality of polyhedral magnets arranged in a Halbachcylinder configuration, the centers of individual ones of the pluralityof polyhedral magnets being arranged substantially in a plane in amagnet rack, the plurality of the polyhedral magnets at least partlyenclosing a testing volume, and wherein a subset of the centers of theindividual ones of the plurality of polyhedral magnets are laterallydisplaced from a nominal position in the magnet rack to counteract amagnetic field gradient of the magnet array.

In an embodiment, the magnet array comprises a pole piece. The polepiece may be adapted to produce the magnetic field gradient.

In an embodiment, the plurality of polyhedral magnets are hexagonalprismatic magnets.

In another embodiment, the magnet array comprises a plurality of magnetracks arranged in a rack stack. In one embodiment, the magnet array mayinclude four magnet racks. In another embodiment, the magnet array mayinclude five magnet racks.

In an embodiment, the magnet rack comprises thirty-six of the hexagonalprismatic magnets. The thirty-six hexagonal prismatic magnets may bearranged in inner, middle, and outer rings of six, twelve and eighteenhexagonal prismatic magnets, respectively, and with the inner hexagonalprismatic magnets being closest to the testing volume.

In an embodiment, the centers of two of the inner ring of six hexagonalprismatic magnets are laterally displaced from the nominal position inthe magnet rack farther away from the testing volume and the centers offour of the inner ring of six hexagonal prismatic magnets are laterallydisplaced from the nominal position in the magnet rack closer to thetesting volume.

In an embodiment, the magnet array may further comprise a first subsetof polyhedral magnets and a second subset of polyhedral magnets, whereinthe first subset and the second subset of polyhedral magnets havedifferent magnetic coercivities.

In an embodiment, the subset of the centers of the individual ones ofthe plurality of polyhedral magnets that are laterally displaced from anominal position in the magnet rack are positioned farther away from thetesting volume.

In an embodiment, the subset of the centers of the individual ones ofthe plurality of polyhedral magnets that are laterally displaced from anominal position in the magnet rack are positioned closer to the testingvolume.

In an embodiment, a first portion of the subset of the centers of theindividual ones of the plurality of polyhedral magnets that arelaterally displaced from a nominal position in the magnet rack arepositioned farther away from the testing volume, and a second portion ofthe subset of the centers of the individual ones of the plurality ofpolyhedral magnets that are laterally displaced from a nominal positionin the magnet rack are positioned closer to the testing volume.

In another aspect there is provided a method for assembling a magnetarray, comprising:

-   -   providing a plurality of polyhedral magnets;    -   providing a cell framework in a magnet rack of the magnet array,        the cell framework for receiving the polyhedral magnets;    -   arranging the plurality of polyhedral magnets in in the cell        framework in the magnet rack, the centers of individual ones of        the plurality of polyhedral magnets being arranged substantially        in a plane in the magnet rack, the plurality of the polyhedral        magnets at least partly enclosing a testing volume, and wherein        a subset of the centers of the individual ones of the plurality        of polyhedral magnets are laterally displaced from a nominal        position in the magnet rack to counteract a magnetic field        gradient of the magnet array; and    -   arranging the magnet rack in a rack stack to assemble the magnet        array.

According to a further aspect, there is provided a magnetic resonancedevice comprising a magnet array comprising a plurality of polyhedralmagnets arranged in a Halbach cylinder configuration, the centers ofindividual ones of the plurality of polyhedral magnets being arrangedsubstantially in a plane in a magnet rack, the plurality of thepolyhedral magnets at least partly enclosing a testing volume, andwherein a subset of the centers of the individual ones of the pluralityof polyhedral magnets are laterally displaced from a nominal position inthe magnet rack to counteract a magnetic field gradient of the magnetarray.

Features and advantages of the subject matter hereof will become moreapparent in light of the following detailed description of selectedembodiments, as illustrated in the accompanying figures. As will berealized, the subject matter disclosed and claimed is capable ofmodifications in various respects, all without departing from the scopeof the claims. Accordingly, the drawings and the description are to beregarded as illustrative in nature, and not as restrictive, and the fullscope of the subject matter is set forth in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present disclosure will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1A is a schematic side view showing a sample tube in an arrangementof superconducting coils for producing a strong magnetic field alignedalong a sample tube's symmetry axis;

FIG. 1B is a schematic top view showing a sample tube in a cylindricalHalbach magnet array viewed along the symmetry axis of the tube;

FIG. 1C is a schematic perspective view showing a sample tube in acylindrical Halbach magnet array viewed along an axis perpendicular tothe symmetry axis of the tube;

FIG. 2 is a cross-sectional view of an idealized Halbach cylinder;

FIGS. 3A-3C are cross-sectional views of implementations of prior artHalbach-cylinder-based magnet assemblies;

FIG. 3D shows an arrangement of pole pieces and shim panels inside acentral cavity within a Halbach cylinder magnet array;

FIG. 4A depicts an idealized magnet configuration for a Halbach sphere;

FIG. 4B shows a practical prior art embodiment of a Halbach sphere;

FIG. 4C is a corner view of a prior art embodiment of a magnet assemblybased on a lattice configuration of polyhedral magnets;

FIG. 5 shows a block diagram of a magnetic resonance device including amagnet array, in accordance with an embodiment of the disclosure;

FIG. 6 shows a top view of an embodiment of a magnet configuration;

FIG. 7A shows a perspective view of the embodiment of FIG. 6illustrating four magnet racks in a rack stack;

FIG. 7B shows a perspective view of an embodiment of a magnet rack stackcomprising five magnet racks;

FIG. 8A shows a top view of an embodiment of a magnet cell framework;

FIG. 8B shows a top view of a further embodiment of a magnet cellframework;

FIG. 8C shows a top view of the embodiment of FIG. 8A, with arrowsillustrating how the positions of a subset of magnets would change fromrespective positions in the embodiment of FIG. 8A to correspondingpositions in the embodiment of FIG. 8B;

FIG. 8D shows a top view of yet another embodiment of a magnet cellframework;

FIG. 8E shows a top view of the embodiment of FIG. 8A, with arrowsillustrating how the positions of a subset of magnets would change fromrespective positions in the embodiment of FIG. 8A to correspondingpositions in the embodiment of FIG. 8D;

FIG. 8F shows a top view of yet a further embodiment of a magnet cellframework;

FIG. 8G shows a top view of the embodiment of FIG. 8A, with arrowsillustrating how the positions of a subset of magnets would change fromrespective positions in the embodiment of FIG. 8A to correspondingpositions in the embodiment of FIG. 8F;

FIG. 9 shows an exploded view of a rack stack comprising multiple magnetracks including the magnet racks of FIGS. 8A, 8B and 8D;

FIG. 10 shows different types of hexagonal prismatic magnets havingdifferent magnetization vectors;

FIG. 11 shows a perspective view of an embodiment of a magnetconfiguration comprising a subset of magnets, each magnet in the subsethaving an out-of-plane magnetization;

FIG. 12A shows an exploded view of an embodiment of multiple magnetracks in a rack stack;

FIG. 12B shows a top view of a third (central) magnet rack of FIG. 12A;

FIG. 12C shows a top view of a second (and fourth) magnet rack of FIG.12A;

FIG. 12D shows a top view of a fifth (bottom) magnet rack of FIG. 12A;

FIG. 12E shows a top view of a first (top) magnet rack of FIG. 12A;

FIG. 13 shows an exploded view of another embodiment of multiple magnetracks in a rack stack; and

FIG. 14 shows a perspective view of an embodiment of a compositepolyhedral magnet.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION

In embodiments there is disclosed a magnet array is disclosed comprisinga plurality of polyhedral magnets arranged in a Halbach cylinderconfiguration, the centers of individual ones of the plurality ofpolyhedral magnets being arranged substantially in a plane in a magnetrack, the plurality of the polyhedral magnets at least partly enclosinga testing volume, and comprising a first plurality of polyhedral magnetsarranged in a Halbach cylinder configuration and a second plurality ofpolyhedral magnets arranged in a non-Halbach configuration. In anotheraspect, a magnet array is disclosed comprising a first subset and asecond subset of polyhedral magnets having different coercivities. Inyet another aspect, a magnet array is disclosed wherein a subset of thecenters of the individual ones of the plurality of polyhedral magnetsare laterally displaced from a nominal position in the magnet rack tocounteract a magnetic field gradient of the magnet array.

The present invention will be more readily understood by referring tothe following examples which are given to illustrate the inventionrather than to limit its scope.

In the present disclosure, the term Halbach cylinder configuration meansa configuration of individual magnets (often called component magnets)disposed around a central volume containing an axis {circumflex over(z)}, in which the magnetization of each magnet is substantiallyoriented according to the equation

{circumflex over (m)}(Σ, ϕ, z)=cos(kϕ){circumflex over(ρ)}+sin(kϕ){circumflex over (ϕ)},

where ρ, φ, z, are the cylindrical polar coordinates of the center ofsaid individual component magnet relative to an origin location and apreferred axis with ϕ=0, and where k is an integer parameter. Amagnetization is “substantially oriented” along a direction if it isexactly oriented along that direction or if it is chosen from a finiteset of possibilities (such as from the set of directions defined byvectors connecting the vertices or the midpoints of edges or faces of afixed polyhedron) as the closest approximation thereto. Those skilled inthe art will recognize k=1 in the equation as the most prevalent case,which produces a substantially uniform magnetic field, directed alongthe preferred ϕ=0 axis, within a portion of the central volume of theconfiguration. FIG. 2 shows magnetization vectors 14 selected accordingto the k=1 case within a region 11 surrounding a central volume 16.

In the present disclosure, the term modified Halbach magnetconfiguration means a configuration (or arrangement) of individualcomponent magnets that comprises two or more subsets of magnets, atleast one subset being configured in a Halbach cylinder magnetconfiguration and at least one other subset having another (non-Halbach)magnet configuration as discussed in this disclosure. In embodiments ofthe present disclosure, such modified Halbach magnet configurationsprovide a design context within which practical implementations ofHalbach cylinders can be improved to provide magnetic fields havingimproved characteristics in applications. A subset of magnets may alsobe referred to as a plurality of magnets or a group of magnets or aportion of magnets.

In the present disclosure, the term magnet rack means a collection ofindividual (component) magnets arranged in a holding structure so thattheir centers lie in a plane. By way of example, FIG. 6 depicts a topview of one embodiment of a magnet rack 250 and individual componentmagnets 210. As shown in FIG. 8A, magnet rack 250 comprises a cellframework 215 and a framework housing 251. In these examples, theindividual component magnets are hexagonal prisms, each of which has asix-fold symmetry axis that is aligned out of the plane of the page. Inembodiments, the individual component magnets may be placed so theircenters coincide with points in a lattice. In the present disclosure,the term lattice refers to a set of points, each of which is displacedfrom an origin by a sum of integer multiples of vectors chosen from abasis set {{circumflex over (v)}₁, {circumflex over (v)}₂, {circumflexover (v)}₃}.

In the present disclosure, magnet rack stack means a collection ofmagnet racks that are stacked along an axis that is perpendicular to thesaid planes containing the centers of the individual component magnetsof the magnet racks. By way of example, FIG. 7A shows a perspective viewof an embodiment of a rack stack 230, with four magnet racks 250. Inembodiments, for example for design or manufacturing purposes, a rackstack may be attached or mounted to additional structures such as a topstructure (not shown in FIG. 7A) or a base structure (260 as shown inFIG. 6 and FIG. 7A). In embodiments, a rack stack may contain 1, 2, 3,4, 5, 6, 7, 8, 9, 10, or any number of magnet racks.

In the present disclosure, individual ones of the polyhedral magnets ina magnet configuration (array) are selected from the group consistingof: a truncated cube; a rhombic dodecahedron; a Platonic solid; anArchimedean solid; a Johnson solid; a prism; a chamfered polyhedron; anda truncated polyhedron. A prism is understood to mean a polyhedroncomprising two opposing congruent n-sided polygonal faces withcorresponding sides of the polygonal faces joined by n rectangularfaces. An example used in this disclosure is a hexagonal prism, whereinn equals 6.

In the present disclosure, a magnetic field gradient is a characteristicof a magnetic field which has a spatial variation in its strength ordirection. In many practical applications, and in particular in magneticresonance applications, a magnet assembly that creates a strong,spatially homogeneous field is desired. In that case, a magnetic field{right arrow over (B)}(x, y, z) is well approximated by its projectionalong an axis, so that the magnetic field is expressed as a scalar valueB_(z), the component of the field along that axis.

In the present disclosure, a quadratic field gradient is a magneticfield gradient in which a component of the field varies in proportion toa second power of some spatial coordinate. For example, a magnetic fieldhaving a z component that is substantially of the form

B _(z)(x, y, z)=B ₀ +a(x ² −y ²)+ . . .

possesses a quadratic field gradient due to its spatial dependence onthe second power of the coordinates x and y. Note that, in the presentdisclosure, “bilinear” gradients such as those exhibited by a field ofthe form

B _(z)(x, y, z)=B ₀ +b(xy)+ . . .

are formally quadratic according to this definition since the functionxy=(u²−v²) when expressed in the linearly related coordinates u=1/2(x+y)and v=1/2(x−y).

In the present disclosure the term magnetic resonance or MR meansresonant reorientation of magnetic moments of a sample in a magneticfield or fields, and includes nuclear magnetic resonance (NMR), electronspin resonance (ESR), magnetic resonance imaging (MRI) and ferromagneticresonance (FMR). Embodiments may also be applied in ion cyclotronresonance (ICR). In particular applications and embodiments, theapparatuses and methods disclosed are applied to NMR and in embodimentsthey are applied to NMR spectrometers or to NMR imagers. Materials thatdisplay magnetic resonance when exposed to a magnetic field are referredto as magnetically resonant or MR active nuclides or materials.

In the present disclosure the terms primary field, main field, primarymagnetic field and main magnetic field mean the magnetic field generatedby a magnet array. In one series of embodiments a field strength in therange of 1.0 to 3.0 Tesla is achieved. However, in alternativeembodiments, the field strength may be below 1.0 Tesla or above 3.0Tesla. The field strength will depend on the number of magnet racks, thestrength of the individual component magnets, the presence or absenceand types of pole pieces, construction materials used, and othervariables.

In embodiments of this disclosure, the magnet array may be comprised ina magnetic resonance apparatus or device. For example, FIG. 5 is anexemplary block diagram of a magnetic resonance device 150 in accordancewith an embodiment of the disclosure. The device 150 comprises acomputer 151 operably connected to a sample rotation control module 152for controlling rotation of an optional sample rotator 154 used forrotating a sample 156 in a sample tube 157 within a sample channel 158provided in the magnet array 159. The computer 151 may also be operablyconnected to a pulsed magnetic field control and signal detection module160 used for controlling a detection coil 162 and receiving a signaltherefrom. The device 150 may also include a field homogeneity controlmodule 164 for controlling the magnetic field in a centrally locatedtesting volume 165. A temperature control module 166 may also beprovided for controlling the temperature of the magnet array 159 and thetemperature inside the channel 158.

In embodiments of the present disclosure, methods are disclosed forbuilding magnet racks, magnet rack stacks, and ultimately magneticresonance devices comprising magnet arrays. Different terms may be usedto describe building magnetic resonance devices based on these magnetarrays, for example, assembling, constructing, producing, manufacturing,or building. These terms refer to building a physical device as opposedto simulating magnet array characteristics.

Magnet Displacements

FIG. 6 shows an example configuration of magnets in a magnet rack 250,shown as a top view. These magnets can be magnetized according to aHalbach cylinder configuration. The magnet array (alternatively known asthe magnet assembly) is generally designated 200. For clarity, themagnet array 200 may include magnets in additional magnet racks notshown in FIG. 6. Individual hexagonal magnets 210 form ahexagonal-cylindrical arrangement surrounding a central cavity 220. InFIG. 6, six magnets are shown in closest proximity to the centralcavity. Additional magnets are positioned farther away from the centralcavity. The size and composition of the individual hexagonal magnets mayvary, e.g., some magnets 210 in the array may be larger than othermagnets 240 in the array. In the example shown in FIG. 6, the smallermagnets 240 may be oriented at a different angle with respect to thelarger magnets 210. The magnets are enclosed by a cell framework in themagnet rack 250, which is positioned on the base 260. In this example,there are 24 larger magnets 210 and twelve smaller magnets 240 in therack; however, other variations in magnet numbers are possible and morethan two types and/or sizes of magnets may be incorporated into theHalbach-based array. In use, a sample will generally be positioned in adefined sample volume, sample space, or testing volume at or close tothe center of the central cavity 220.

One way to increase the strength of a magnetic field in a magnet arrayis to use pole pieces, which can acquire a magnetic polarization whenplaced in a magnetic field. This polarization can increase the strengthof the magnetic field in the region of space near the pole piece to avalue that is larger than it would be in the absence of the pole piece.Sometimes in applications it is desirable to use pole pieces in pairsrather than individually. FIG. 3D shows a known example configuration ofpole pieces 54 within a hexagonal cavity defined by a set of six magnets52, each of which is in the shape of a hexagonal prism.

FIG. 7A is a perspective view of the magnet assembly of FIG. 6, showinga stack 230 of four cylindrical racks 250 above the base 260, with eachrack having an arrangement of magnets as shown in FIG. 6. Other numbersof racks, e.g., one, two, three, four, or five racks, can be used, andthe magnet arrangement in each rack may be the same or different fromthe other racks. As an example, FIG. 7B shows a perspective view of astack 235 of five racks 255. Exposed in the figure is a top rack havingan alternative magnet configuration 201 to that which is shown in FIG. 6and FIG. 7A. As shown in FIG. 7B, thirty-six hexagonal prismatic magnets210 may be arranged in inner, middle, and outer rings of six, twelve andeighteen hexagonal prismatic magnets, respectively, and with the innerhexagonal prismatic magnets being closest to the central cavity, whichin an NMR spectrometer may include a sample testing volume. Just asdifferent numbers of magnet racks may be included in a magnet rackstack, although thirty-six magnets are illustrated in this example,other numbers, arrangements, and types of magnets may be used in amagnet configuration as described herein.

FIG. 8A illustrates a rack 250 comprising a cell framework 215 and aframework housing 251. The cell framework 215 is to be considered anominal framework in this disclosure against which other frameworks canbe compared. An example of a function of the cell framework is to guidethe placement of individual component magnets in the magnet rack 250during assembly of the rack. Another example of a function of theframework is to provide separation between some or all magnets in therack. In other words, the cell framework defines a number of cells, eachcell for receiving an individual component magnet into the magnet rack.In other embodiments, a cell in a cell framework may receive a compositemagnet as disclosed herein.

In a non-limiting example, the magnet racks are 1.5″ in height, as arethe hexagonal prismatic magnets within the racks (1.5″ along thesix-fold symmetry axis of the hexagonal prism). The cells in the cellframework are 1.25″ across (from the midpoint of one edge to themidpoint of the opposing edge across a hexagonal face), and the wallsmaking up the framework itself are 0.030″ thick. In alternativeembodiments, the magnet dimensions and cell framework dimensions may belarger or smaller depending on the application and the desired magneticfield strength.

As shown in FIG. 8A, the cell framework 215 defines multiple cells, theinnermost six of which, surrounding the central cavity, are labelled Afor convenience. This framework 215 can accept up to thirty-six magnetspositioned around the central cavity 220. The framework 215 includesframework sections 217 which are connected to one another throughframework vertices 221. (Note: not all framework sections and verticesare explicitly labelled in the figure.) A Cartesian coordinate axissystem is shown in FIG. 8A with the x-axis being directed out of theplane of the page, and this axis system can be understood to carrythrough FIGS. 8B-8G.

FIG. 8B illustrates a modified cell framework 316 within a rack 350.This framework 316 can also accept up to thirty-six magnets positionedaround a central cavity 320. However, framework 316 includes fewerframework sections 317 and fewer framework vertices 321 than are shownin framework 215 in FIG. 8A. In particular, some framework sectionsbetween individual magnet cells labelled C, and between magnet cellslabelled C and the central cavity of the framework, are absent. Thisremoval permits the magnets placed in cells labelled C to be closer tothe central cavity and closer to each other. Moreover, frameworksections between cells labelled B and adjacent cells, on the sides ofthe cells labelled B opposite the central cavity 320, are also removed.This removal permits the magnets placed in cells labelled B to befurther away from the central cavity. In embodiments of the presentdisclosure, framework sections (e.g., section 318) may have a thinnerwidth than other framework sections (e.g., section 319). In anon-limiting example, if the nominal framework wall thickness is 0.030″,then this sets the range of displacements to values roughly in therange±0.030″. In alternative embodiments, the range of displacementswill be similarly constrained by the mechanical characteristics selectedfor the framework.

These in-plane (lateral) displacements of the centers of the magnetsfrom the nominal framework depicted in FIG. 8A may produce a quadraticfield gradient opposite in sign to a quadratic field gradient producedby the insertion of pole pieces into the magnet configuration.Therefore, considered placement of component magnets into the frameworkcan be implemented to counteract the quadratic field gradient producedby the pole pieces. FIG. 8C more clearly shows (in the form of arrows)the directions of displacements just described for the framework 316 inFIG. 8B compared to the framework 215 in FIG. 8A.

Alternative modifications to the cell framework can be made to influencethe magnetic field and magnetic field gradients. By way of illustrationand not limitation, FIG. 8D shows an alternative embodiment of amodified cell framework 422 within a rack 450. This framework 422 canaccept a plurality of magnets positioned around a central cavity 420.The framework 422 is different from the framework 316 and from theframework 215. The framework 422 includes fewer framework sections 417and the same number of framework vertices 421 compared to framework 215.FIG. 8E shows (in the form of arrows) the magnet displacements (thechange in magnet positions) effected by the framework shown in FIG. 8Dcompared to the framework shown in FIG. 8A.

FIG. 8F illustrates yet a further alternative embodiment of a modifiedcell framework 523. FIG. 8G shows with arrows how positions of a subsetof magnets would change from the framework of FIG. 8A to the frameworkof FIG. 8F.

The differences in the example frameworks shown in FIGS. 8B, 8D and 8Fcompared to the nominal framework that is shown in FIG. 8A may be viewedas distortions of the nominal framework. The nominal framework exhibitsequal spacing between the magnets, and the distortions can render thespacing between magnets unequal. Such distortions may amplify ordiminish certain magnetic field gradients that would be imposed by theinsertion of pole pieces, mitigating deleterious consequences of thegradients on the main magnetic field. This capability may allow for agreater range of pole piece shapes compatible with various applications.For instance, the distorted frameworks may counteract deleteriouseffects on magnetic field gradients of pole pieces positioned in thecentral cavity and create an overall improvement of magnetic fieldhomogeneity and strength.

In an embodiment of the present disclosure, a magnet rack stack maycomprise individual magnet racks comprising the same framework ordifferent frameworks. Selection of the framework for each individualmagnet rack in a magnet rack stack may be determined based on factorssuch as an understanding of magnetic field gradients of the magnet array(and which of the magnetic field gradients may require suppression),ease of magnet array assembly, cost of assembly, or other technicaland/or practical factors. FIG. 9 shows an exploded view of onenon-limiting example of a magnet rack stack 535 comprising five magnetracks. The top and bottom (first and fifth when counting from the top)magnet racks are shown to comprise the nominal framework 215 of FIG. 8A,while in this example rack stack 535, two magnet racks (the second andfourth) comprise the distorted framework 316 of FIG. 8B, and the central(third) magnet rack in FIG. 9 comprises the distorted framework 422 ofFIG. 8D. While FIG. 9 exhibits a top-to-bottom symmetry that may beadvantageous in some applications, other applications may require orbenefit from an anti-symmetric or asymmetric arrangement, for examplewherein the framework is different in each rack.

The modified Halbach magnet arrays disclosed may be physically assembled(e.g., into a magnet rack, magnet rack stack, or magnetic resonancedevice). In an embodiment of the present disclosure, a method forassembling a magnet array comprises providing a physical set ofpolyhedral magnets and providing a cell framework in a magnet rack ofthe magnet array, the cell framework for receiving the polyhedralmagnets. The method comprises arranging these polyhedral magnets in thecell framework in the magnet rack. The centers of the polyhedral magnetsin the magnet rack may be arranged substantially in a plane in themagnet rack of the magnet array and such that the polyhedral magnets atleast partly enclose a testing volume that would, in use, accommodate achemical sample for analysis. In this method, a subset of the centers ofthe polyhedral magnets are laterally displaced (following the structureof the cell framework) from a nominal position in the magnet rack tocounteract a magnetic field gradient of the magnet array. The method mayfurther comprise arranging the magnet rack in a rack stack to assemblethe magnet array.

The modified Halbach magnet arrays disclosed, including the associatedmagnet rack and magnet rack stack examples shown in FIGS. 6-9, may beused in a magnetic resonance device, for example, as shown in FIG. 5.The magnetic resonance device may comprise a magnet array comprising aplurality of polyhedral magnets arranged in a Halbach cylinderconfiguration, the centers of individual ones of the plurality ofpolyhedral magnets being arranged substantially in a plane in a magnetrack, the plurality of the polyhedral magnets at least partly enclosinga testing volume, and wherein a subset of the centers of the individualones of the plurality of polyhedral magnets are laterally displaced froma nominal position in the magnet rack to counteract a magnetic fieldgradient of the magnet array.

Magnet Coercivity

Permanent magnet materials can be subject to magnetic stresses(demagnetizing forces) when the magnets are placed in strong magneticfields, for example, when magnets are placed so that their magnetizationvectors are aligned in opposition with the magnetic fields produced bynearby strong magnets. Magnets that are under such stress can be subjectto partial or full demagnetization, and this deleterious effect can beexacerbated at elevated temperatures. The resistance to this effect isquantified for a particular magnetic material by its intrinsic magneticcoercivity (also called intrinsic coercivity) H_(c,i). Often, when theword coercivity is used without qualification, the term is understood tomean intrinsic coercivity. The SI units of coercivity are ampere permeter (A/m) and the cgs units of coercivity are Oersted. It is commonlythe case that magnets that have high coercivity (greater resistance todemagnetization) are costly compared to magnets that have lowcoercivity. To optimize performance and cost in constructing magnetarrays for applications including NMR spectroscopy, it is thereforeadvantageous to know in what locations within a magnet configuration onemay use magnets of high coercivity and in what locations one may usemagnets of low coercivity. For example, magnets exhibiting highcoercivity may be desirable in locations in a magnet array wheremagnetic fields are strong and in opposition to the magnetization of themagnets themselves. Such placement of high coercivity magnets may reducethe tendency of magnets in such locations to demagnetize or may increasethe practical range of temperatures over which a device incorporatingthe magnet array may be used.

Commercial manufacturers typically specify magnet materials by grade,and this grade is associated with a coercivity label. For example, onemay purchase grades N42, N42M, N42H, N42SH, N42UH, N42EH, and N42AH. Thecoercivity of each grade increases as one goes through this list.Between successive grades in the list, the coercivity can vary by 20% ormore. Within a grade, the coercivity typically varies by less than a fewpercent. In this disclosure, magnets of “the same” coercivity areunderstood to mean magnets of the same commercial grade, having avariation in coercivity not exceeding 5% and preferably not exceeding2%. In this disclosure, magnets of “different” coercivity are understoodto mean magnets of different grades, where the difference between thecoercivities exceeds at least a threshold of 10% and preferably athreshold of 20%.

Another important characteristic of magnetic materials and componentmagnets made from these materials is the remanent magnetization. Thisquantity is the magnetization present in a magnetic material after ithas been magnetized during manufacture. Often instead of remanentmagnetization a manufacturer, for example, will specify a proportionalquantity, the remanent field, B_(r). Remanent magnetization is importantin magnet array design and applications because it effectivelycharacterizes the “strength” of a component magnet and the ability ofthe magnet to produce a magnetic field at a location outside of thespace the magnet occupies.

It is often the case that the strongest available magnets, those havingthe highest “maximum energy product,” the maximum attainable product ofthe magnetic flux density and the magnetic field strength, are subjectto a trade-off between high remanent magnetization and high coercivity.It is therefore an aspect of the present disclosure to use knowledge ofoverall magnetic fields present within a magnet array, and in particularwithin the volume occupied by individual component magnets, to identifylocations (also referred to as positions or sites in the array) havingrelatively weak coercive stress in order to select magnets of lowercoercivity and low cost (or correspondingly high remanent magnetization)in order to either increase the available overall magnetic fieldproduced within a central testing volume of the array or to reduce theoverall cost of a device incorporating the magnet array.

Disclosed herein is a figure of merit, a threshold coercivity H_(T). Theintrinsic coercivity H_(c,i) of the magnetic material to be used for acomponent magnet at a given site in a magnet array must exceed thisthreshold coercivity.

At a point {right arrow over (r)} inside a magnetic material, threevectorial quantities are defined: the magnetic field intensity {rightarrow over (H)}({right arrow over (r)}), the magnetization {right arrowover (M)}({right arrow over (r)}), and the magnetic flux density {rightarrow over (B)}({right arrow over (r)}). These are related by therelation

${{\overset{\rightarrow}{H}\left( \overset{\rightarrow}{r} \right)} = {{\frac{1}{\mu_{0}}{\overset{\rightarrow}{B}\left( \overset{\rightarrow}{r} \right)}} - {\overset{\rightarrow}{M}\left( \overset{\rightarrow}{r} \right)}}},$

where μ₀ is the permittivity constant. When a magnet is under coercivestress, {right arrow over (H)} and {right arrow over (M)} point inroughly opposite directions over a significant portion of the volumewithin the magnet. In this case, the dot product of these vectors willbe negative. Therefore, the criterion for stability in the presence ofdemagnetizing forces is that the quantity −{right arrow over (H)}·{rightarrow over (M)} not be too large anywhere within the magnet.

Bjørk, et al. have considered the problem of demagnetization in magnetarrays and give

${{- \mu_{0}}\frac{\overset{\rightarrow}{H} \cdot \overset{\rightarrow}{M}}{B_{r}}} \geq H_{c,i}$

as a criterion for estimating when a magnet is under coercive stresslarge enough to cause demagnetization. (See R. Bjørk, A. Smith, and C.Bahl, “The efficiency and the demagnetization field of a general Halbachcylinder,” Journal of Magnetism and Magnetic Materials vol. 384, p. 128,2015, and especially equation (8) therein.)

For use in reliable magnet products, this criterion is not stringentenough. Magnet assemblies must be robust to temperature changes (forexample during shipping of a commercial product) and to tolerances inspecifications associated with manufacture of the magnetic materials,component magnets, holding structures, and the like.

To account for such factors, each component magnet having amanufacturer-specified coercivity H_(c,i) ^(θ) ^(spec) (given at aspecified standard temperature θ_(spec), for example 20° C.) mustsatisfy the following inequality:

${{- \mu_{0}}\frac{\left\lbrack {{\overset{\rightarrow}{H}\left( \overset{\rightarrow}{r} \right)} \cdot {\overset{\rightarrow}{M}\left( \overset{\rightarrow}{r} \right)}} \right\rbrack_{\min}}{B_{r}}} \leq {{\alpha\left( {1 - {k\Delta T}} \right)}H_{c,i}^{\theta_{spec}}}$

where [{right arrow over (H)}({right arrow over (r)})·{right arrow over(M)}({right arrow over (r)}]_(min) is the minimum (most negative) valueof the dot product {right arrow over (H)}·{right arrow over (M)} withinthe magnet, α is a safety factor (for example 90% (0.90)), k is themagnetic material's coercivity temperature coefficient (for example0.0056° C.⁻¹), and ΔT is the difference between a maximum operatingtemperature and the standard temperature used in the specification ofcoercivity. Also disclosed herein is the following equation definingthreshold coercivity:

$H_{T} = {{- \mu_{0}}{\frac{\left. \left. \left\lbrack {{{\overset{\rightarrow}{H}\left( \overset{\rightarrow}{r} \right)} \cdot \overset{\rightarrow}{M}}\overset{\rightarrow}{r}} \right. \right) \right\rbrack_{\min}}{{\alpha\left( {1 - {k\Delta T}} \right)}B_{r}}.}}$

The manufacturer-specified coercivity for a magnet at a given site mustexceed H_(T) for that site to meet the performance criteria mentionedabove.

In an embodiment of the present disclosure, a coercivity selectionmethod comprises the steps of:

-   1. Setting up a magnetostatic simulation with component magnets in    specified locations and with the orientation of their magnetization    vectors according to a proposed modified Halbach magnet    configuration-   2. For each component magnet location    -   2.1. Choosing a set of points within the magnet volume        associated with said magnet location    -   2.2. Running said magnetostatic simulation to obtain the field        intensity {right arrow over (H)}({right arrow over (r)}) at each        point {right arrow over (r)} in said set of points and assigning        to {right arrow over (M)}({right arrow over (r)}) the        magnetization {right arrow over (M)} associated to the        orientation according to the proposed modified Halbach        configuration    -   2.3. Calculating the product {right arrow over (H)}({right arrow        over (r)})·{right arrow over (M)}({right arrow over (r)})_at        each point in said set of points    -   2.4. Selecting the minimum (most negative) value [{right arrow        over (H)}({right arrow over (r)})·{right arrow over (M)}({right        arrow over (r)})]_(min) for said component magnet location    -   2.5. Calculating the threshold coercivity

$H_{T} = {{- \mu_{0}}\frac{\left\lbrack {{\overset{\rightarrow}{H}\left( \overset{\rightarrow}{r} \right)} \cdot {\overset{\rightarrow}{M}\left( \overset{\rightarrow}{r} \right)}} \right\rbrack_{\min}}{\overset{¯}{{\alpha ⁡\left( {1-{k⁢\Delta ⁢T}} \right)}⁢B_{r}}}}$

for said component magnet location

-   -   2.6. Selecting an available (physical) component magnet having a        coercivity exceeding H_(T) for said location

Commercially available simulation software can be adapted to performStep 1. Non-limiting examples of such software include products byCOMSOL and products by Ansys, Inc.

In a second embodiment, the steps of the nominal embodiment are precededby the step (Step 0) of assigning each component magnet location to asymmetry class of locations, with each location related to the othermembers of its assigned symmetry class by a symmetry element of theassembly as a whole, such as a reflection plane, rotation axis,rotation-reflection axis, or inversion center, or a magnetic reflectionplane, magnetic rotation axis, magnetic rotation-reflection axis, ormagnetic inversion center. Step 2 of the nominal method is thenperformed on each symmetry class of locations.

As in the theory of symmetry for magnetic materials (see for example M.Hamermesh, Group Theory and its Application to Physical Problems, Dover,N.Y., 1989), in this disclosure, the term magnetic symmetry element,which includes magnetic reflection plane, magnetic rotation axis,magnetic rotation-reflection axis, or magnetic inversion center, isunderstood to mean the corresponding symmetry element followed byreversal of currents and corresponding reversal of the direction ofmagnetization.

In a further embodiment, replace step 2.6 in the second embodiment witha conditional step (2.6-A) as follows:

-   (2.6-A) If the threshold coercivity is above a desired maximum    coercivity H_(max), then choose an alternate orientation {right    arrow over (M)}_(alt) for the magnetization at said symmetry class    of locations and repeat Step 2. Otherwise select an available    (physical) component magnet having a coercivity exceeding H_(T) for    each of said magnets in said symmetry class of locations.

In an embodiment of the present disclosure, a magnet array may comprisetwo subsets of polyhedral magnets, one subset having magnets of arelatively higher coercivity compared to a second subset of magnetshaving a relatively lower coercivity. The first subset of polyhedralmagnets having the higher coercivities may be positioned closer to atesting volume in the array and the second subset of polyhedral magnetshaving the lower coercivities may be positioned farther from the testingvolume.

The number of polyhedral magnets in the first subset having the highercoercivities, the coercivity values, and the sites within the magnetarray in which the first subset is arranged, may be selected accordingto a simulation such as a magnetostatic simulation. Likewise, the numberof polyhedral magnets in the second set having the lower coercivities,the coercivity values, and the sites within the magnet array in whichthe second subset is arranged, may also be specified by the simulation.The sites in the array that are selected for magnets with elevatedcoercivity may be determined to coincide with those sites that exhibitstronger demagnetizing forces in the simulation and the sites in thearray that are selected for magnets with diminished coercivity may bedetermined to coincide with those sites that exhibit weakerdemagnetizing forces in the simulation. Further examples pertaining tocoercivity are discussed in the next section.

Magnetization Vectors

In the present disclosure, a magnet having a magnetization vector lyingin the plane defining a magnet rack (for example, in the yz plane shownin FIG. 8A) is said to be diametrically magnetized. A magnet having amagnetization vector perpendicular to the plane of the magnet rack issaid to be axially magnetized. A magnet having a magnetization vectorthat does not lie in the plane, but is not perpendicular to the plane,is said to be obliquely magnetized. A magnet that is either axiallymagnetized or obliquely magnetized is said to possess out-of-planemagnetization.

FIG. 10 shows examples of magnets that are in the shape of hexagonalprisms. In FIG. 10, magnet A is a diametrically face-magnetized magnet,wherein the magnetization vector (indicated by an arrow) is normal to arectangular side face of the magnet and perpendicular to the six-foldsymmetry axis of the hexagonal face of the magnet. Magnet B isdiametrically edge-magnetized, wherein the magnetization vector isperpendicular to the six-fold rotational symmetry axis of the hexagonalface of the magnet and extends from a long edge bounding a rectangularface of the magnet to the opposite edge across the body of the magnet.It will be readily appreciated that this vector is also parallel tocertain opposing rectangular faces of the magnet B. FIG. 10 also shows amagnet E, which is axially magnetized, that is, magnetized along avector that is coincident with the six-fold symmetry axis of the magnet.

Magnets C and D are examples of obliquely magnetized magnets. Moreprecisely, magnet C is obliquely edge magnetized, wherein themagnetization vector extends from the midpoint of one edge bounding ahexagonal face of the magnet to the midpoint of the opposite edgebounding the opposite hexagonal face of the magnet and across the centerof the magnet. It will be appreciated from FIG. 10 that themagnetization vector of magnet C is perpendicular to said edges and thatthe magnetization vector forms an acute angle with the six-fold symmetryaxis of magnet C. Magnet D is obliquely vertex magnetized, having amagnetization vector that extends from one vertex, through the center ofthe magnet, to the opposite vertex. The magnetization vector of magnet Dalso forms an acute angle with the six-fold symmetry axis of magnet D.

In a Halbach cylinder magnet configuration, such as the ones depicted inFIGS. 1B, 3A-D, and 5, all magnets are diametrically magnetized. Thatis, the magnetization vectors have only radial and azimuthal componentsand therefore lie in the plane of a corresponding magnet rack or otherholding structure.

In the present disclosure, modified Halbach magnet configurations aredescribed which comprise a first subset of magnets in a Halbach cylinderconfiguration and a second subset of magnets that may include axially orobliquely magnetized magnets or diametrically magnetized magnets thatotherwise deviate from the magnetization prescribed by a strict Halbachcylinder configuration. Including the second subset of magnets with thefirst subset of magnets may advantageously increase the magnetic fieldstrength within a sample testing volume at least partially enclosed bythe magnet configuration.

By way of illustration and not limitation, FIG. 11 shows a rack 650 inperspective view comprising two subsets of hexagonal prismatic magnetsaccording to an embodiment of the present disclosure. The first subsetof magnets, shown with black arrows and designated 631, arediametrically magnetized and form a Halbach cylinder configurationaround a central volume 620. Magnets in the second of the two subsetsare not diametrically magnetized, but, rather, are axially (641 and645), obliquely-edge (670) and obliquely-vertex (661) magnetized in thisexample, as shown interspersed within the rack 650. Each magnet is heldwithin the magnet rack 650 at a fixed location by the cell framework615.

In general, a magnet configuration according to an embodiment of thepresent disclosure comprises multiple subsets of magnets. A first subsetcomprises magnets that are diametrically magnetized and orientedaccording to a Halbach cylinder configuration. A second subset (andfurther third or fourth or more subsets) of magnets comprise magnetsthat are not magnetized according to a Halbach cylinder configuration.These second and further subsets comprise magnets that may be magnetizedaxially, obliquely, or diametrically.

In embodiments, a magnet at displacement {right arrow over (r)} within asubset can be chosen so that its magnetization is aligned substantiallyaccording to a spherical Halbach configuration, that is, as determinedby the formula:

{circumflex over (m)}=(2({circumflex over (v)}·{right arrow over(r)}){circumflex over (r)}−({right arrow over (r)}·{right arrow over(r)}){circumflex over (v)})/({right arrow over (r)}·{right arrow over(r)}),

where {circumflex over (v)} is a preferred field direction, and where{circumflex over (r)} is the unit vector pointing along {right arrowover (r)}. In embodiments the magnetization can be chosen from a finiteset of possibilities consistent with limiting the choices of magnettypes to a symmetrical set such as those depicted in FIG. 10 for ahexagonal prismatic magnet.

FIGS. 12A-E collectively show an example of a magnet rack stack andassociated magnet racks according to an embodiment of the presentdisclosure. FIG. 12A shows a magnet rack stack 700 of five cylindricalracks in exploded view. The racks are stacked so that their centersalign along a central axis 710. The rack stack comprises a first (top)rack 750, two intermediate racks 730 (second and fourth in order fromthe top of the rack stack), a third (central) rack 720, and a fifth(bottom) rack 740. Each rack is shown in top view in one of FIGS. 12B-E.In this example, the second and fourth racks have the same type andarrangement of magnets, therefore, FIG. 12C shows the two racks' commonconfiguration in top view. While the top and bottom racks (750 and 740,respectively) are different, FIGS. 12D (bottom) and 12E (top) show thatthese two racks are mirror images of one another, with the mirror planelying in the center of rack 720 in FIG. 12A and perpendicular to theaxis 710. The axis 710 coincides with the x axis exhibited in each ofthe coordinate frames 723, 733, 743, 753 shown in FIGS. 12B-E,respectively.

FIG. 12B is a top view of central rack 720 of FIG. 12A, and this rack asa whole has a symmetry plane coinciding with the plane of the page inFIG. 12B. Because the second and fourth (intermediate) racks have thesame type and arrangement of magnets, and the top and bottom racks aremirror images of one another, the rack stack as a whole (FIG. 12A)exhibits a mirror symmetry plane perpendicular to axis 710 andcoinciding with the center of rack 720.

In FIG. 12B, which shows the third (central) rack 720 in top view,hexagonal prismatic component magnets are arranged within a frameworkhousing 721, with a magnetization vector indicated for each magnet inthe rack by arrows 722. Some of the magnets, e.g., 724, belong to asubset of magnets that are strictly magnetized along a vector prescribedby a Halbach cylinder configuration. Some of the magnets, e.g., 725,belong to a subset of magnets that are magnetized along a vector that isa closest approximation to a Halbach cylinder configuration given aconstraint that the magnetization be chosen from the finite set ofpossibilities shown for a hexagonal prism in FIG. 10. The six centrallylocated magnets 726 are shown in a Halbach cylinder configuration, andthese magnets belong to a subset of magnets that have elevatedcoercivity relative to other magnets in the magnet assembly. A furthersubset of magnets, e.g., 727, exhibit magnetization vectors that do notstrictly conform to a Halbach cylinder configuration, but, rather, arereoriented in order to decrease the threshold coercivity for thoselocations in the magnet rack. At those locations, a reduced thresholdcoercivity H_(T) (and magnet expense) is permitted at the cost of areduced magnetic field in the center bore (central volume) 760 as aresult of deviation of the magnets 727 from the strict Halbach cylindermagnetization orientation. Overall, the third (central) magnet rack 720includes an arrangement of twenty diametrically face magnetized magnetsand sixteen diametrically edge magnetized magnets, all of which havein-plane magnetization.

FIG. 12C shows one intermediate (second and fourth) rack 730 in topview. As in central rack 720, in intermediate racks 730, hexagonalprismatic component magnets are arranged within a framework housing 731,with a magnetization vector indicated for each magnet in the rack byarrows 732. A subset of magnets, e.g., 734, are strictly magnetizedalong a vector prescribed by a Halbach cylinder configuration. Some ofthe magnets, e.g., 735, belong to a subset of magnets that aremagnetized along a vector that is a closest approximation to a Halbachcylinder configuration given a constraint that the magnetization bechosen from the finite set of possibilities shown for a hexagonal prismin FIG. 10. The six centrally located magnets 736 exhibit a Halbachcylinder configuration, and these magnets belong to the subset ofmagnets that have elevated coercivity relative to other magnets in themagnet assembly. In contrast to FIG. 12B, magnets 737 in magnet rack730, whose counterparts 727 in the central rack 720 exhibit reorientedmagnetization vectors in order to decrease the threshold coercivityH_(T) for those locations, are not reoriented in FIG. 12C. In theintermediate racks, the threshold coercivity requirement is lessstringent than in the central rack. Overall, the second and fourth(intermediate) magnet racks 730 include an arrangement of twenty-eightdiametrically face magnetized magnets and eight diametrically edgemagnetized magnets, all of which have in-plane magnetization.

FIG. 12D shows bottom (fifth) rack 740 in top view. As in the centralmagnet rack 720 and intermediate racks 730, hexagonal prismaticcomponent magnets are arranged in rack 740 within a framework housing741, with a magnetization vector indicated for each magnet in the rackby arrows 742. A subset of magnets, e.g., 744, are strictly magnetizedalong a vector prescribed by a Halbach cylinder configuration. Some ofthe magnets, e.g., 745, belong to a subset of magnets that aremagnetized along a vector that is a closest approximation to a Halbachcylinder configuration given a constraint that the magnetization bechosen from the finite set of possibilities shown for a hexagonal prismin FIG. 10. Two of the six centrally located magnets 746 belong to thesubset of magnets that have elevated coercivity relative to othermagnets in the magnet assembly. These magnets 746, along with othertypes of magnets 747 and 748, exhibit magnetization vectors that deviatesubstantially from their counterparts in the central and intermediateracks 720 and 730, respectively. These magnets 746, 747 and 748, belongto a subset of magnets whose magnetization vectors are determinedsubstantially according to a spherical Halbach configuration andformula. Again, in this context ‘substantially’ means that themagnetization vectors are selected from the finite set of possibilitiesexhibited in FIG. 10. Some of the magnets in this subset, e.g., 747 and748, exhibit magnetizations that are out-of-plane. In particular, thesemagnets are axially magnetized. In FIG. 12D, this is shown for magnets748 by a circle enclosing a cross (to indicate magnetization into theplane of the page) and for magnets 747 by a circle enclosing a dot (toindicate magnetization out of the plane of the page).

FIG. 12E shows top (first) rack 750 in top view. Magnet rack 750 is themirror image of magnet rack 740, the mirror plane being the plane of thepage, i.e., the yz-plane according to the coordinate axes 743 and 753.Overall, the first and fifth (top 750 and bottom 740, respectively)magnet racks each include an arrangement of fourteen diametrically facemagnetized magnets, four diametrically edge magnetized magnets, and 18axially magnetized magnets. In other words, there are eighteen magnetshaving an in-plane magnetization vector and eighteen magnets having anout-of-plane magnetization vector in each of the first and fifth racks.

According to another embodiment of the present disclosure, a furtherexample of a magnet rack stack is provided in exploded view in FIG. 13.In FIG. 13, a rack stack 800 having five identical racks 730 is shown.The racks are aligned with their centers along an axis 810. Returning toFIG. 12C, all component magnets in magnet rack 730 are magnetizedsubstantially in a Halbach cylinder configuration. The magnets aredivided (portioned or grouped) into two subsets according to whethertheir coercivities are relatively elevated (higher) or relatively notelevated (lower).

In the foregoing example embodiments, sites in magnet racks are occupiedby polyhedral magnets, in particular hexagonal prismatic magnets. Inother embodiments, selected sites may be occupied by pluralities ofmagnets, wherein said pluralities are together substantially shaped toconform to the shape of the site as a whole. Each magnet in theplurality of magnets may be selected from a finite set of possibilities,such as the set shown in FIG. 10 for the hexagonal prism. FIG. 14 showsan example embodiment in which an overall hexagonal prismatic site 900is occupied by a plurality containing two smaller hexagonal prismaticmagnets 910 and 920. Magnets 910 and 920 have two differentmagnetization vectors 915 and 925, respectively, and magnet 910 isaxially magnetized, whereas magnet 920 is obliquely edge magnetized. Inthis disclosure, the terms composite magnet and composite polyhedralmagnet are understood to mean a plurality of magnets in a cell orlattice site in a magnet assembly where each of the plurality of magnetshas its own magnetization vector. The plurality of magnets is togethershaped so as to conform to a single cell or lattice site. Use of acomposite magnet in a site can increase the effective range ofpossibilities for the effective average magnetization vector within acell or lattice site and the corresponding contribution made to themagnetic field within a magnet assembly's testing volume. While FIG. 14shows a plurality containing two magnets, other composite magnets mayinclude a plurality of more than two magnets.

The modified Halbach magnet arrays disclosed may be physically assembled(e.g., into a magnet rack, magnet rack stack, or magnetic resonancedevice). In an embodiment of the present disclosure, a method forassembling a magnet array comprises providing a first physical set ofpolyhedral magnets and arranging these polyhedral magnets in a Halbachcylinder magnet configuration in a magnet rack. The centers of the firstphysical set of polyhedral magnets in a magnet rack may be arrangedsubstantially in a plane in the magnet array and such that thepolyhedral magnets at least partly enclose a testing volume that would,in use, accommodate a chemical sample for analysis. The method furthercomprises providing a second physical set of polyhedral magnets in themagnet rack and arranging the second set of polyhedral magnets in themagnet rack in a non-Halbach configuration. The method may furthercomprise arranging the magnet rack in a rack stack to assemble themagnet array.

The modified Halbach magnet arrays disclosed, including the associatedmagnet rack and magnet rack stack examples shown in FIGS. 11-14, may beused in a magnetic resonance device, for example, as shown in FIG. 5.

The magnetic resonance device may comprise a magnet array comprising afirst plurality of polyhedral magnets arranged in a Halbach cylinderconfiguration, the centers of individual ones of the plurality ofpolyhedral magnets being arranged substantially in a plane in a magnetrack of the magnet array, the plurality of polyhedral magnets at leastpartly enclosing a testing volume, and a second plurality of polyhedralmagnets in the magnet rack, the second plurality of magnets arranged ina non-Halbach configuration.

The magnetic resonance device may comprise a magnet array comprising aplurality of polyhedral magnets arranged in a magnet configuration, theplurality of polyhedral magnets comprising a first subset of polyhedralmagnets and a second subset of polyhedral magnets, the plurality ofpolyhedral magnets at least partly enclosing a testing volume, andwherein the first subset and the second subset of polyhedral magnetshave different magnetic coercivities.

While preferred embodiments have been described above and illustrated inthe accompanying drawings, it will be evident to those skilled in theart that modifications may be made without departing from thisdisclosure. Such modifications are considered as possible variantscomprised in the scope of the disclosure.

1-38. (canceled)
 39. A magnet array comprising: a first plurality ofpolyhedral magnets arranged in a Halbach cylinder configuration, thecenters of individual ones of the plurality of polyhedral magnetsarranged substantially in a plane in a magnet rack of the magnet array,the plurality of polyhedral magnets at least partly enclosing a testingvolume; and a second plurality of polyhedral magnets in the magnet rack,the second plurality of magnets arranged in a non-Halbach configuration.40. The magnet array of claim 39, the second plurality of polyhedralmagnets in the magnet rack comprising magnets having an in-planemagnetization vector, an out-of-plane magnetization vector, or acombination thereof.
 41. The magnet array of claim 39 having anassociated magnetic field with a designated field direction {circumflexover (v)}, wherein the magnetization direction {circumflex over (m)} ofat least one of the second plurality of polyhedral magnets located at adisplacement vector {right arrow over (r)} from an origin point in thetesting volume is determined by the formula:{circumflex over (m)}=(2({circumflex over (v)}·{right arrow over(r)}){circumflex over (r)}−({right arrow over (r)}·{right arrow over(r)}){circumflex over (v)})/({right arrow over (r)}·{right arrow over(r)}), where {circumflex over (r)} is the unit vector pointing along{right arrow over (r)}.
 42. The magnet array according to claim 39,wherein individual ones of said polyhedral magnets are selected from thegroup consisting of: a truncated cube, a rhombic dodecahedron, aPlatonic solid, an Archimedean solid, a Johnson solid, a prism, achamfered polyhedron, and a truncated polyhedron.
 43. The magnet arrayof claim 40, the second plurality of polyhedral magnets comprisingmagnets that are obliquely edge magnetized, obliquely vertex magnetized,axially magnetized, or a combination thereof.
 44. The magnet array ofclaim 39, the first plurality of magnets comprising magnets that arediametrically face magnetized, diametrically edge magnetized, or acombination thereof.
 45. The magnet array of claim 39, wherein the firstand second pluralities of polyhedral magnets are hexagonal prismaticmagnets.
 46. The magnet array of any one of claim 39, comprising aplurality of magnet racks arranged in a rack stack.
 47. The magnet arrayof claim 46, comprising five magnet racks.
 48. The magnet array of claim39, the magnet rack comprising a cell framework and a framework housing.49. The magnet array of claim 48, the magnet rack and the first andsecond pluralities of polyhedral magnets each having a height of 3.81cm.
 50. The magnet array of claim 48, cells in the cell framework havinga width of 3.175 cm and walls of the cell framework having a thicknessof 0.0762 cm.
 51. The magnet array of claim 46, wherein a first magnetrack arranged above a central magnetic reflection plane of the rackstack has a first magnet configuration that is a magnetic reflection ofa second magnet configuration of a second magnet rack arranged below thecentral magnetic reflection plane of the rack stack.
 52. The magnetarray of claim 47, the first plurality of polyhedral magnets in each ofthe first and fifth magnet racks comprising fourteen diametrically facemagnetized magnets and four diametrically edge magnetized magnets, andthe second plurality of polyhedral magnets in each of the first andfifth magnet racks comprising eighteen axially magnetized magnets. 53.The magnet array of claim 47, wherein each of the second and fourthmagnet racks comprise twenty-eight diametrically face magnetized magnetsand eight diametrically edge magnetized magnets.
 54. The magnet array ofclaim 47, wherein the third magnet rack comprises twenty diametricallyface magnetized magnets and sixteen diametrically edge magnetizedmagnets.
 55. The magnet array of claim 39, further comprising a firstsubset of polyhedral magnets and a second subset of polyhedral magnets,wherein the first subset and the second subset of polyhedral magnetshave different magnetic coercivities.
 56. The magnet array of claim 39further comprising at least one composite magnet.
 57. The magnet arrayof claim 56, wherein the at least one composite magnet includes two ormore magnets each having a different magnetization vector and the two ormore magnets are together sized and shaped to be positioned in anindividual cell of the magnet array.
 58. A magnetic resonance devicecomprising a magnet array comprising a first plurality of polyhedralmagnets arranged in a Halbach cylinder configuration, the centers ofindividual ones of the plurality of polyhedral magnets being arrangedsubstantially in a plane in a magnet rack of the magnet array, theplurality of polyhedral magnets at least partly enclosing a testingvolume, and a second plurality of polyhedral magnets in the magnet rack,the second plurality of magnets arranged in a non-Halbach configuration.59. A method for assembling a magnet array, comprising: providing afirst plurality of polyhedral magnets; arranging the first plurality ofpolyhedral magnets in a Halbach cylinder configuration in a magnet rack,the centers of individual ones of the plurality of polyhedral magnetsbeing arranged substantially in a plane in the magnet rack, theplurality of polyhedral magnets at least partly enclosing a testingvolume; providing a second plurality of polyhedral magnets; arrangingthe second plurality of polyhedral magnets in a non-Halbachconfiguration in the magnet rack; and arranging the magnet rack in arack stack to assemble the magnet array.